Package dev.nm.stat.stochasticprocess.multivariate.random

Class MultivariateBrownianRRG

java.lang.Object

dev.nm.stat.stochasticprocess.multivariate.random.MultivariateBrownianRRG

All Implemented Interfaces:

Seedable, MultivariateRandomRealizationGenerator

public class MultivariateBrownianRRG
extends Object
implements MultivariateRandomRealizationGenerator

This is the Random Walk construction of a multivariate Brownian motion.

For constant μ and σ, this method is exact in the sense that the joint distribution of the simulated values coincides with the joint distribution of the corresponding Brownian motion a the time grid points. Please note that this says nothing about what happens between two successive grid points.

For time-dependent μ and σ, this method in general introduce discretization error even at the time grid points, because the increments will no longer have exactly the correct mean and variance.

Constructor Summary

Constructors

Constructor	Description
MultivariateBrownianRRG(int d, int T)	Construct a random realization generator to produce multi-dimensional Brownian paths at evenly spaced time points [0, 1, ...].
MultivariateBrownianRRG(int d, TimeGrid timePoints)	Construct a random realization generator to produce multi-dimensional Brownian paths at time points specified.
MultivariateBrownianRRG(int d, TimeGrid timePoints, Vector initial)	Construct a random realization generator to produce multi-dimensional Brownian paths at time points specified.

Method Summary

Modifier and Type	Method	Description
MultivariateRealization	nextRealization()	Construct a realization of a multivariate stochastic process.
void	seed(long... seeds)	Seed the random number/vector/scenario generator to produce repeatable experiments.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

MultivariateBrownianRRG

public MultivariateBrownianRRG(int d,
 TimeGrid timePoints,
 Vector initial)

Construct a random realization generator to produce multi-dimensional Brownian paths at time points specified.

Parameters:

d - the dimension of the Brownian motion

timePoints - specifying the time points in a grid

initial - the initial value of the process

MultivariateBrownianRRG

public MultivariateBrownianRRG(int d,
 TimeGrid timePoints)

Construct a random realization generator to produce multi-dimensional Brownian paths at time points specified.

Parameters:

d - the dimension of the Brownian motion

timePoints - specifying the time points in a grid

MultivariateBrownianRRG

public MultivariateBrownianRRG(int d,
 int T)

Construct a random realization generator to produce multi-dimensional Brownian paths at evenly spaced time points [0, 1, ...].

Parameters:

d - the dimension of the Brownian motion

T - the number of time points

Method Details

seed

public void seed(long... seeds)

Description copied from interface: Seedable

Seed the random number/vector/scenario generator to produce repeatable experiments.

Specified by:

seed in interface Seedable

Parameters:

seeds - the seeds

nextRealization

public MultivariateRealization nextRealization()

Description copied from interface: MultivariateRandomRealizationGenerator

Construct a realization of a multivariate stochastic process.

Specified by:

nextRealization in interface MultivariateRandomRealizationGenerator

Returns:

a realization